• Title, Summary, Keyword: Moments

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Derivatio of Optimal Design Flood by L-Moments and LH-Moments(II) - On the method of LH-Moments - (L-모멘트 및 LH-모멘트 기법에 의한 적정 설계홍수량의 유도(II)-LH-모멘트법을 중심으로)

  • 이순혁
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.41 no.3
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    • pp.41-50
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    • 1999
  • Derivatio of reasonable design floods was attempted by comparative analysis of design floods derived by Generalized Extreme Value(GEV) distribution using methods of L-moments and LH-moments for the annual maximum series at ten watersheds along Han, Nagdong. Geum, Yeongsan and Seomjin river systems, LH-coefficient of variation, LH-skewness and Lh-kurtosis were calcualted by KH-moment ration respectively. Paramenters were estimated by the Method of LH-Moments, Design floods obtained by Method of LH-Moments using different methods for plotting positionsi n GEV distribution and design floods were compared with those obtained using the Method of L-Moments by the Relative Mean Errors(RME) and Relative Absolute Errors(RAE). The results was found that design floods derived by the method of L-Moments and LH-Moments using Cunnane plotting position formula in the GEV distribution are much closer to those of the observed data in comparison with those obtained by methods of L-moments and LH-moments using the other formula for plotting positions from the viewpoint of Relative Mean Errors and Relative Absolute Errors. In viewpoint of the fact that hydrqulic structures including dams and levees are genrally using design floods with the return period of two hundred years or so, design floods derived by LH-Moments are seemed to be more reasonable than those of L-Moments in the GEV distribution.

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Derivation of Design Flood by L-Moments and LH-Moments in GEV distributiion (L-모멘트 및 LH-모멘트에 의한 GEV 분포모형의 실계홍수량의 유도)

  • 이순혁;박명근;맹승진;정연수;김동주;류경식
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • pp.479-485
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    • 1999
  • This study was conducted to derived design floods by Generalized Extreme Value(GEV) distributiion for the annual maximum series at ten watersheds along Han, Nagdong, Geum , Yeongsan and Seomjin river systems. Adequency for the analysis of flood data used in this study was established by the test of Independence, Homogeneity , detection of Outliers. Coefficient of variation , skewness and kurtosis were calculated by the L-Moment, and LH-Moment ratio respectively. Parameters were estimated by the Method of L-Method of LH-Moment. Design floods obtained by Method of L-Moments and LH-Moments using different methods for plotting positions in GEV distributions and were compared with those obatined using the Method of L-Moments and LH-Moments by the Relative Mean Errors and Realtive Absoulte Errors. It was found that desgin floods derived by the method of L-Moments and LH-Moments using Cunnane plotting position foumula in the GEV distribution are much closer to those of the observed data in comparison with those obtained by methods of L-moments and LH-moments using the other formula for poltting postions from the viewpoint of Relative Mean Errors and Relative Absoulte Errors. In view of the fact that hydraulic structures indcluding dams and levees are generally usiong design floods with the return period of two hundred years or so, design floods derived by LH-Moments are seemed to be more reasonable than those of L-Moments in the GEV distribution.

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Derivation of Optimal Design Flood by L-Moments and LB-Moments ( I ) - On the method of L-Moments - (L-모멘트 및 LH-모멘트 기법에 의한 적정 설계홍수량의 유도( I ) - L-모멘트법을 중심으로 -)

  • 이순혁;박명근;맹승진;정연수;김동주;류경식
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.40 no.4
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    • pp.45-57
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    • 1998
  • This study was conducted to derive optimal design floods by Generalized Extreme Value (GEV) distribution for the annual maximum series at ten watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was established by the tests of Independence, Homogeneity, detection of Outliers. L-coefficient of variation, L-skewness and L-kurtosis were calculated by L-moment ratio respectively. Parameters were estimated by the Methods of Moments and L-Moments. Design floods obtained by Methods of Moments and L-Moments using different methods for plotting positions in GEV distribution were compared by the Relative Mean Errors(RME) and Relative Absolute Errors(RAE). The results were analyzed and summarized as follows. 1. Adequacy for the analysis of flood data was acknowledged by the tests of Independence, Homogeneity and detection of Outliers. 2. GEV distribution used in this study was found to be more suitable one than Pearson type 3 distribution by the goodness of fit test using Kolmogorov-Smirnov test and L-Moment ratios diagram in the applied watersheds. 3. Parameters for GEV distribution were estimated using Methods of Moments and L-Moments. 4. Design floods were calculated by Methods of Moments and L-Moments in GEV distribution. 5. It was found that design floods derived by the method of L-Moments using Weibull plotting position formula in GEV distribution are much closer to those of the observed data in comparison with those obtained by method of moments using different formulas for plotting positions from the viewpoint of Relative Mean Errors and Relative Absolute Errors.

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Bending moments in raft of a piled raft system using Winkler analysis

  • Jamil, Irfan;Ahmad, Irshad
    • Geomechanics and Engineering
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    • v.18 no.1
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    • pp.41-48
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    • 2019
  • Bending moments in the raft of a pile raft system is affected by pile-pile interaction and pile-raft interaction, amongst other factors. Three-Dimensional finite element program has to be used to evaluate these bending moments. Winkler type analysis is easy to use but it however ignores these interactions. This paper proposes a very simplified and novel method for finding bending moments in raft of a piled raft based on Winkler type where raft is supported on bed of springs considering pile-pile and pile-raft interaction entitled as "Winkler model for piled raft (WMPR)" The pile and raft spring stiffness are based on load share between pile and raft and average pile raft settlement proposed by Randolph (1994). To verify the results of WMPR, raft bending moments are compared with those obtained from PLAXIS 3D software. A total of sixty analysis have Performed varying different parameters. It is found that raft bending moments obtained from WMPR closely match with bending moments obtained from PLAXIS 3D. A comparison of bending moments ignoring any interaction in Winkler model is also made with PLAXIS-3D, which results in large difference of bending moments. Finally, bending moment results from eight different methods are compared with WMPR for a case study. The WMPR, though, a simple method yielded comparable raft bending moments with the most accurate analysis.

On Bounds for Moments of Unimodal Distributions

  • Sharma, R.;Bhandaria, R.
    • Communications for Statistical Applications and Methods
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    • v.21 no.3
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    • pp.201-212
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    • 2014
  • We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

Estimation of Design Flood by the Determination of Best Fitting Order for LH-Moments (LH-모멘트의 차수에 따른 설계홍수량 추정)

  • Maeng, Sung-Jin;Lee, Soon-Hyuk
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • pp.233-236
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    • 2002
  • This study was conducted to estimate the design flood by the determination of best fitting order for LH-moments of the annual maximum series at fifteen watersheds. Parameters of GEV distribution and flood flows of return period n years were derived by the methods of L, L1, L2, L3 and L4-moments. Frequency analysis of flood flow data generated by Monte Carlo simulation was performed by the methods of L, L1, L2, L3 and L4-moments using GEV distribution. Relative Root Mean Square Error (RRMSE), Relative Bias (RBIAS) and Relative Efficiency (RE) using methods of L, L1, L2, L3 and L4-moments for GEV distribution were computed and compared with those resulting from Monte Carlo simulation. At almost all of the watersheds, the more the order of LH-moments and the return periods increased, the more RE became, while the less RRMSE and RBIAS became. Consequently, design floods for the applied watersheds were derived by the methods of L3 and L4-moments among LH-moments in view of high confidence efficiency.

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Higher Order Moments of Record Values From the Inverse Weibull Lifetime Model and Edgeworth Approximate Inference

  • Sultan, K.S.
    • International Journal of Reliability and Applications
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    • v.8 no.1
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    • pp.1-16
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    • 2007
  • In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

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Estimation of Design Flood by the Determination of Best Fitting Order of LH-Moments(II) (LH-모멘트의 적정 차수 결정에 의한 설계홍수량 추정(II))

  • 맹승진;이순혁
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.45 no.1
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    • pp.33-44
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    • 2003
  • This study was conducted to estimate the design flood by the determination of best fitting order for LH-moments of the annual maximum series at fifteen watersheds. Using the LH-moment ratios and Kolmogorov-Smirnov test, the optimal regional probability distribution was identified to be the Generalized Extreme Value (GEV) in the first report of this project. Parameters of GEV distribution and flood flows of return period n years were derived by the methods of L, L1, L2, L3 and L4-moments. Frequency analysis of flood flow data generated by Monte Carlo simulation was performed by the methods of L, L1, L2, L3 and L4-moments using GEV distribution. Relative Root Mean Square Error. (RRMSE), Relative Bias (RBIAS) and Relative Efficiency (RE.) using methods of L, Ll , L2, L3 and L4-moments for GEV distribution were computed and compared with those resulting from Monte Carlo simulation. At almost all of the watersheds, the more the order of LH-moments and the return periods increased, the more RE became, while the less RRMSE and RBIAS became. The Absolute Relative Reduction (ARR) for the design flood was computed. The more the order of LH-moments increased, the less ARR of all applied watershed became It was confirmed that confidence efficiency of estimated design flood was increased as the order of LH-moments increased. Consequently, design floods for the appled watersheds were derived by the methods of L3 and L4-moments among LH-moments in view of high confidence efficiency.

Derivation of Optimal Design Flood by L-Moments (L-모멘트법에 의한 적정 설계홍수량의 유도)

  • 이순혁;박명근;맹승진;정연수;김동주;류경식
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • pp.318-324
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    • 1998
  • This study was conducted to derive optimal design floods by Generalized Extreme-value(GEV) distribution for the annual maximum series at ten watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was established by the tests of Independence, Homogeneity, detection of Outliers. L-coefficient of variation, L-skewness and L-kurtosis were calculated by L-moment ratio respectively. Parameters were estimated by the Methods of Moments and L-Moments. Design floods obtained by Methods of Moments and L-Moments using different methods for plotting positions in GEV distribution were compared by the relative mean and relative absolute error. It was found that design floods derived by the method of L-moments using weibull plotting position formula in GEV distribution are much closer to those of the observed data in comparison with those obtained by method of moments using different formulas for plotting positions in view of relative mean and relative absolute error.

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